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Draw three equal line segments in a unit circle to divide the circle into four parts of equal area.

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Investigate constructible images which contain rational areas.

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A spiropath is a sequence of connected line segments end to end taking different directions. The same spiropath is iterated. When does it cycle and when does it go on indefinitely?

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Two perpendicular lines lie across each other and the end points are joined to form a quadrilateral. Eight ratios are defined, three are given but five need to be found.

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Two polygons fit together so that the exterior angle at each end of their shared side is 81 degrees. If both shapes now have to be regular could the angle still be 81 degrees?

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Where should runners start the 200m race so that they have all run the same distance by the finish?

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What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?

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Investigate x to the power n plus 1 over x to the power n when x plus 1 over x equals 1.

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Use trigonometry to determine whether solar eclipses on earth can be perfect.

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In a snooker game the brown ball was on the lip of the pocket but it could not be hit directly as the black ball was in the way. How could it be potted by playing the white ball off a cushion?

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What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?

Fancy learning a bit more about rates of reaction, but don't know where to look? Come inside and find out more...

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Have you got the Mach knack? Discover the mathematics behind exceeding the sound barrier.

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Explore the properties of combinations of trig functions in this open investigation.

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How much peel does an apple have?

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What's the chance of a pair of lists of numbers having sample correlation exactly equal to zero?

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Can you find some Pythagorean Triples where the two smaller numbers differ by 1?

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Explore the properties of this different sort of differential equation.

Challenge Level

Unearth the beautiful mathematics of symmetry whilst investigating the properties of crystal lattices

Dip your toe into the fascinating topic of genetics. From Mendel's theories to some cutting edge experimental techniques, this article gives an insight into some of the processes underlying. . . .

Read about the mathematics behind the measuring devices used in quantitative chemistry

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In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.

Challenge Level

Work with numbers big and small to estimate and calculate various quantities in biological contexts.

Challenge Level

Work with numbers big and small to estimate and calculate various quantities in physical contexts.

This article (the first of two) contains ideas for investigations. Space-time, the curvature of space and topology are introduced with some fascinating problems to explore.

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Get some practice using big and small numbers in chemistry.

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Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?

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Take any pair of numbers, say 9 and 14. Take the larger number, fourteen, and count up in 14s. Then divide each of those values by the 9, and look at the remainders.

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Formulate and investigate a simple mathematical model for the design of a table mat.

An introduction to a useful tool to check the validity of an equation.

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See how enormously large quantities can cancel out to give a good approximation to the factorial function.

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Ever wondered what it would be like to vaporise a diamond? Find out inside...

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Look at the advanced way of viewing sin and cos through their power series.

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Looking at small values of functions. Motivating the existence of the Taylor expansion.

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Build up the concept of the Taylor series

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Which parts of these framework bridges are in tension and which parts are in compression?

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Given the equation for the path followed by the back wheel of a bike, can you solve to find the equation followed by the front wheel?

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By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.

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How fast would you have to throw a ball upwards so that it would never land?

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We all know that smoking poses a long term health risk and has the potential to cause cancer. But what actually happens when you light up a cigarette, place it to your mouth, take a tidal breath. . . .

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Get further into power series using the fascinating Bessel's equation.

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Work out the numerical values for these physical quantities.